ON THE COFINALITY OF THE LEAST λ-STRONGLY COMPACT CARDINAL

Abstract

In this paper, we characterize the possible cofinalities of the least λ -strongly compact cardinal. We show that, on the one hand, for any regular cardinal, δ, that carries a λ -complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above δ, that the least λ -strongly compact cardinal has cofinality δ. On the other hand, provably the cofinality of the least λ -strongly compact cardinal always carries a λ -complete uniform ultrafilter.

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Authors/Creators:	You, Z Yuan, J
Copyright, Publisher and Additional Information:	© The Author(s), 2023. This article has been published in a revised form in https://doi.org/10.1017/jsl.2023.4. This version is free to view and download for private research and study only. Not for re-distribution or re-use.
Keywords:	λ-strongly compact cardinal, cofinality, iterated ultrapower, Radin forcing
Dates:	Accepted: 13 January 2023 Published (online): 19 January 2023
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User:	Symplectic Publications
Date Deposited:	23 Mar 2023 10:32
Last Modified:	25 Jun 2023 23:17
Status:	Published online
Publisher:	Cambridge University Press
Identification Number:	https://doi.org/10.1017/jsl.2023.4

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ON THE COFINALITY OF THE LEAST λ-STRONGLY COMPACT CARDINAL

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